Question

use the product property to multiply. assume all variables represent positive real numbers.

\\(\sqrt{2x} \cdot \sqrt{13y}\\)

\\(\sqrt{2x} \cdot \sqrt{13y} = \square\\)
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Apply the product property of radicals

The product property of radicals states that for any non-negative real numbers \(a\) and \(b\):

$$ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} $$

Apply this property to the given expression:

$$ \sqrt{2x} \cdot \sqrt{13y} = \sqrt{2x \cdot 13y} $$

Step 2: Multiply the terms inside the radical

Multiply the coefficients and the variables together:

$$ 2 \cdot 13 = 26 $$

$$ x \cdot y = xy $$

Combine them under a single radical:

$$ \sqrt{26xy} $$

Since \(26\) has no perfect square factors other than \(1\), the expression cannot be simplified further.

Answer:

$$ \sqrt{26xy} $$